The Theory of Money and Credit - Ludwig von Mises [16]
The credit of having exposed the error contained in the identification of these two last propositions belongs to Cuhel. The judgment that so many small satisfactions are outweighed by a satisfaction of another kind is in fact not identical with the judgment that the one satisfaction is so many times greater than one of the others. The two would be identical only if the satisfaction afforded by a number of commodity units taken together were equal to the satisfaction afforded by a single unit on its own multiplied by the number of units. That this assumption cannot hold good follows from Gossen's law of the satisfaction of wants. The two judgments, "I would rather have eight plums than one apple" and "I would rather have one apple than seven plums," do not in the least justify the conclusion that Böhm-Bawerk draws from them when he states that therefore the satisfaction afforded by the consumption of an apple is more than seven times but less than eight times as great as the satisfaction afforded by the consumption of a plum. The only legitimate conclusion is that the satisfaction from one apple is greater than the total satisfaction from seven plums but less than the total satisfaction from eight plums. [3]
This is the only interpretation that can be harmonized with the fundamental conception expounded by the marginal-utility theorists, and especially by Böhm-Bawerk himself, that the utility (and consequently the subjective use-value also) of units of a commodity decreases as the supply of them increases. But to accept this is to reject the whole idea of measuring the subjective use-value of commodities. Subjective use-value is not susceptible of any kind of measurement.
The American economist Irving Fisher has attempted to approach the problem of value measurement by way of mathematics. [4] His success with this method has been no greater than that of his predecessors with other methods. Like them, he has not been able to surmount the difficulties arising from the fact that marginal utility diminishes as supply increases, and the only use of the mathematics in which he clothes his arguments, and which is widely regarded as a particularly becoming dress for investigations in economics, is to conceal a little the defects of their clever but artificial construction.
Fisher begins by assuming that the utility of a particular good or service, though dependent on the supply of that good or service, is independent of the supply of all others. He realizes that it will not be possible to achieve his aim of discovering a unit for the measurement of utility unless he can first show how to determine the proportion between two given marginal utilities. If, for example, an individual has a hundred loaves of bread at his disposal during one year, the marginal utility of a loaf to him will be greater than if he had one hundred and fifty loaves. The problem is, to determine the arithmetical proportion between the two marginal utilities. Fisher attempts to do this by comparing them with a third utility. He therefore supposes the individual to have B gallons of oil annually as well, and calls ² that increment of B whose utility is equal to that of the 100th loaf of bread. In the second case, when not a hundred but a hundred and fifty loaves are available, it is assumed that the supply of B remains unchanged.